fibonacci everywhere ?

Well, I have come across this sequence before in csc148 where I wrote a program to calculate Fib(n). As to its applications, I would really be interested to know more about that. I mean sooner or later theory must show where it is applied. This sequence and its sum F(n+2) - 1 is more interesting to work with as it is less linear and thereby more challenging.

It was valuable to see the re-arrangement of the function in the definition of the function without changing the overall result. Makes me look at things with a different perspective in mind when trying to tackle a proof. Though not evident at first because of the procedural thinking that we are taught by, it soon becomes another method of approach.

Maybe we should think differently and instead of coming up with solutions in a procedural form try using some simple algorithm whose logic derives the very essence of what we are trying to prove. Perhaps then we would not need to make bulky and highly inefficient applications. There is a limit as to how much you can optimize a procedure. Although some people look at algorithms as procedures in mathematical terms and therefor see no difference.

Assignment 1 and missed lecture

I missed this week's lecture. I really dislike missing lectures, as it takes me extra time to catchup to the material I missed. Looking at the notes it seems I missed the introduction to the Principle of Well Ordering. I can sort of see how knowing that there exists a smallest value can induce a proof for some problems. I found it quite interesting to know that simple induction, principle of well ordering, and complete induction are all correlated. In the proofs of the relations between the principles I see that we use the anticedant for each proof, however is there a way to not use the anticedant?

second week - different forms of induction

Missed the first hour of the lecture because of a lab I needed to attend. Looking at all the different methods of induction, I am surprised there was no way shown to transition between them. What are some other types of inductions not covered here? I am slowly picking up the proof structure again for A1. The notes that the professor put up really helped! Overall I feel pretty confident in the course.

the theory of computation

I was surprised to see a change in tactics from the professor. His new tablet appeared to me as another channel for communications which proved to be quite effective. I managed to enjoy the introduction much more then initially anticipated. It appears like there is significant difference for the student whether or not the professor tries to engage the class in the topic (like taking input from the class). I for instance sometimes have to do a presentation at work and find it quite difficult to come up with the perfect way to explain everything in the time constraints that I have so I found that by having input from the viewers every short amount of time the presentation seems more enjoyable and people leave with less gaps in the mind about the subject. One other thing that seems interesting is that we have now more flexibility with the proof structure. Which is great considering how long my proofs were in the previous year.